Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Özkan Öztürk; Elvan Akın

Nonautonomous Dynamical Systems (2016)

  • Volume: 3, Issue: 1, page 1-13
  • ISSN: 2353-0626

Abstract

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We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

How to cite

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Özkan Öztürk, and Elvan Akın. "Nonoscillation Criteria for Two-Dimensional Time-Scale Systems." Nonautonomous Dynamical Systems 3.1 (2016): 1-13. <http://eudml.org/doc/276928>.

@article{ÖzkanÖztürk2016,
abstract = {We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.},
author = {Özkan Öztürk, Elvan Akın},
journal = {Nonautonomous Dynamical Systems},
keywords = {Time-scale systems; Nonoscillation; Dynamic Equations; time-scale systems; nonoscillation; dynamic equations},
language = {eng},
number = {1},
pages = {1-13},
title = {Nonoscillation Criteria for Two-Dimensional Time-Scale Systems},
url = {http://eudml.org/doc/276928},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Özkan Öztürk
AU - Elvan Akın
TI - Nonoscillation Criteria for Two-Dimensional Time-Scale Systems
JO - Nonautonomous Dynamical Systems
PY - 2016
VL - 3
IS - 1
SP - 1
EP - 13
AB - We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.
LA - eng
KW - Time-scale systems; Nonoscillation; Dynamic Equations; time-scale systems; nonoscillation; dynamic equations
UR - http://eudml.org/doc/276928
ER -

References

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  1. [1] D. R. Anderson, Oscillation and Nonoscillation Criteria for Two-dimensional Time-Scale Systems of First-Order Nonlinear Dynamic Equations. Electron. J. Differential Equations, Vol. 2009 (2009), No. 24, pp 1-13.  Zbl1185.34140
  2. [2] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston, 2001.  Zbl0978.39001
  3. [3] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, 2003.  Zbl1025.34001
  4. [4] P. G. Ciarlet, Linear and Nonlinear Functional Analysis with Applications. Siam, 2013.  
  5. [5] T. S. Hassan, Oscillation Criterion for Two-Dimensional Dynamic Systems on Time Scales. Tamkang J. Math., Volume 44 (2013), Number 3, 227-232.  Zbl1291.34163
  6. [6] B. Knaster, Un th´eor`eme sur les fonctions d’ensembles. Ann. Soc. Polon. Math. 6 (1928)133-134.  Zbl54.0091.04
  7. [7] Ö. Öztürk and E. Akın, Classification of Nonoscillatory Solutions of Nonlinear Dynamic Equations on Time Scales. Dynam. Systems. Appl. To appear, 2015.  
  8. [8] Ö. Öztürk, E. Akın and I. U. Tiryaki, On Nonoscillatory Solutions of Emden-Fowler Dynamic Systems on Time Scales. FILOMAT. To appear, 2015.  
  9. [9] W. Li, S. Cheng, Limiting Behaviors of Non-oscillatory Solutions of a Pair of Coupled Nonlinear Differential Equations. Proc. Edinb. Math. Soc. (2000) 43, 457-473.  Zbl0979.34029
  10. [10] W. Li, Classification Schemes for Nonoscillatory Solutions of Two-Dimensional Nonlinear Difference Systems. Comput.Math. Appl. 42 (2001) 341-355. [Crossref] Zbl1006.39013
  11. [11] X. Zhang, Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales. International Journal of Mathematical, Computational, Natural and Physcial Enginnering Vol:8 (2014), No:1.  
  12. [12] S. Zhu and C. Sheng, Oscillation and nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales. Discrete Dynamics in Nature and Society , Volume 2012, Article ID 137471.  

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